Asymptotic analysis of a family of Sobolev orthogonal polynomials related to the generalized Charlier polynomials

TL;DR

This paper investigates the asymptotic behavior of Sobolev orthogonal polynomials related to generalized Charlier weights, providing asymptotic expansions involving falling factorial polynomials within a nonstandard inner product framework.

Contribution

It introduces an asymptotic analysis of Sobolev orthogonal polynomials associated with generalized Charlier weights using a nonstandard inner product involving the forward difference operator.

Findings

Derived asymptotic expansion for the polynomials.

Identified the role of falling factorial polynomials in the asymptotics.

Extended understanding of Sobolev orthogonal polynomials with nonstandard inner products.

Abstract

In this paper we tackle the asymptotic behavior of a family of orthogonal polynomials with respect to a nonstandard inner product involving the forward operator {\Delta}. Concretely, we treat the generalized Charlier weights in the framework of {\Delta}--Sobolev orthogonality. We obtain an asymptotic expansion for this orthogonal polynomials where the falling factorial polynomials play an important role.